The present invention relates generally to missile guidance.
The traditional approach to missile guidance is to use Proportional Navigation (PRONAV). PRONAV was developed by C. Yuan at RCA Laboratories during World War II using physical intuition [1]. The resulting simplistic guidance law states that the commanded linear acceleration a.sub.c is proportional to the line-of-sight (LOS) rate .sigma..sub.T. The proportionality constant can be broken down into the product of the effective navigation ratio N times the relative missile-target closing velocity Vc, EQU a.sub.c =NV.sub.c.sigma..sub.T (1)
Two decades later, the quasi-optimality of PRONAV was derived [2]. The prefix quasi is used here because of all the assumptions that must be made in deriving PRONAV as a solution of a linear-quadratic optimal control problem [3]. These assumptions are as follows:
1. The target has zero acceleration. PA1 2. The missile has perfect response and complete control of its acceleration vector. PA1 3. The missile is launched on a near collision course such that the line-of-sight (LOS) angles remain small over the entire engagement. PA1 4. The missile has zero acceleration along the LOS over all time. PA1 U.S. Pat. No. 5,168,277--LaPinta et al PA1 U.S. Pat. No. 5,062,056--Lo et al PA1 U.S. Pat. No. 5,035,375--Friedenthal et al PA1 U.S. Pat. No. 4,993,662--Barnes et al PA1 U.S. Pat. No. 4,980,662--Eiden PA1 U.S. Pat. No. 4,959,800--Woolley PA1 U.S. Pat. No. 4,825,055--Pollock PA1 U.S. Pat. No. 4,719,584--Rue et al PA1 U.S. Pat. No. 4,568,823--Dielh et al PA1 U.S. Pat. No. 4,402,250--Baasch PA1 U.S. Pat. No. 4,162,775--Voles PA1 Yuan, C. L., "Homing and Navigation Courses of Automatic Target-Seeking Devices," Journal of Applied Physics, Vol. 19, Dec. 1948, pp. 1122-1128. PA1 Fossier, M. W., "The Development of Radar Homing Missiles," Journal of Guidance, Control, and Dynamics, Vol. 7, Nov-Dec 1984, pp. 641-651, PA1 Zarchan, P., Tactical and Strategic Missile Guidance, Volume 124, Progress in Astronautics and Aeronautics, Published by the American Institute of Aeronautics and Astronautics, Inc., Washington D.C. PA1 [1] Yuan, C. L., "Homing and Navigation Courses of Automatic Target-Seeking Devices," RCA Labs, Princeton, N.J., Report PTR-12C, Dec 1942. PA1 [2] Bryson, A.E. and Ho, Y.C., Applied Optimal Control, Blaisdell Publishing Company, Waltham, Mass. 1969. PA1 [3] Riggs, T. L. and Vergez, P. L., "Advanced Air-to-Air Missile Guidance Using Optimal Control and Estimation," USAF Armament Laboratory, AFATL-TR-81-52, June 1981. PA1 [4] Lin, C.F., Modern Navigation, Guidance, and Control Processing, Prentice Hall, Englewood Cliffs, N.J., 1991. PA1 [5] D'Souza, C.N., McClure, M.A., and Cloutier, J.R., "Spherical Target State estimators," Proceedings of the American Control Conference, Baltimore, Md., June 1944. PA1 [6] Proportional Guidance (PROGUIDE), and Augmented Proportional Guidance (AUGMENTED PROGUIDE) (See my said co-pending application Ser. No. 08/233,588, filed Apr. 26, 1994. PA1 [7] Anderson, B.D.O. and Moore, J.B., Optimal Control, Prentice Hall, Englewood Cliffs, N.J., 1990. PA1 [8] D'Souza, C.N., McClure, M.A., and Cloutier, J.R., "Bank-to-Turn In-House Control Study (BANCS)," Final report t the AMRAAM JSPO, June 1944. PA1 [9] McClure, M.A. and D'Souza, C.N., "Integrated Guidance and Estimation Methodology Bank-to-Turn AMRAAM," (Restricted) Proceedings of the AIAA Missile Sciences Conference, Monterey, Calif., November 1944.
In order to remove the first assumption, an additional term is added to the basic PRONAV equation in an attempt to account for target acceleration. The additional term is simply the target's estimated linear acceleration a.sub.T multiplied by a proportionality gain g3. In order to remove the fourth assumption, another term is sometimes included which attempts to compensate for missile slowdown a.sub.M. The resulting guidance law, known as augmented PRONAV, is given in its most general form as EQU a.sub.c =NV.sub.c.sigma.g3(t.sub.go)a.sub.T +g.sub.4 (t.sub.go)a.sub.M (2)
where g.sub.3 and g.sub.4 are functions of t.sub.go, which is the time remaining or time-to-go until impact or detonation. Using Assumption 3, an alternative form EQU a.sub.c =g1(t.sub.go)y+g2(t.sub.go) y+g3[t.sub.go ]a.sub.T +g4(t.sub.go)a.sub.M (3)
can be derived, where y is relative position and y is relative velocity, with g1=N/t.sub.go.sup.2 and g2=N/t.sub.go.
Over the past twenty-five years, numerous linear-quadratic (LQ) optimal control problems have been posed attempting to improve upon augmented PRONAV and determine "optimal" values for the gains g1,g2,g3 and g4 (See ref. [4], Chapter 8). These LQ formulations have all been based on Cartesian-based target motion models and the resulting guidance law solutions all require knowledge of time-to-go.
There are two disadvantages associated with this type of guidance law development. The first disadvantage is that states in a Cartesian-based target motion are nonlinearly related to the seeker measurements which are spherical-based quantities, such as range, range rate, and azimuth and elevation angles. Thus, there is a certain amount of incompatibility between the seeker measurements and the target motion model. The second disadvantage is the requirement to estimate t.sub.go. A consistently accurate estimate of t.sub.go cannot be obtained in a maneuvering target scenario since it depends upon the target's future motion, which is unknown.
In order to make the target state estimator more compatible with the seeker measurements and overcome the first disadvantage, a spherical-based target motion model was developed in reference [5]. Unfortunately, this model has nonlinear kinematics and if these kinematics were directly used in a posed optimal guidance law problem, the nonlinear control problem would have to be solved numerically in an iterative fashion. Furthermore, such a solution could not be obtained in real time on a missile-sized microprocessor.
In my co-pending application Ser. No. 08/233,588, filed Apr. 26, 1994, t.sub.go was eliminated in the development of guidance laws known as proportional guidance (PROGUIDE) and augmented proportional guidance (Augmented PPROGUIDE). However these guidance laws are not based on a nonlinear model of the target's motion and do not command flight path angle rate or linear acceleration. Instead they are based on a simple linear model of the target's motion and command flight path angle acceleration.
The following United States patents are of interest.
None of the cited patents disclose Adaptive Matched Augmented Proportional Navigation which are based on two guidance law algorithms. The patent to Pollock discloses the use of a trajectory correction algorithm for object tracking. The remaining patents describe a variety of different tracking methods which are of less interest.
The following prior publications are of interest.
The following prior publications of interest are referenced in the specification by the indicated reference number.